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@misc{biasseL13,
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@Article{shaffer,
	author = {M. Jacobson and  \'{A}. Pint\'{e}r and P. Walsh},
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	journal = {Mathematics of computation},
	year = 2003,
	volume = {72},
	pages = {2099--2110}
}

@inproceedings {Buchmann,
   author       = {J. Buchmann},
   title        = {A Subexponential Algorithm for the Determination of Class
                  Groups and Regulators of Algebraic Number Fields},
   booktitle    = {S\'eminaire de Th\'eorie des Nombres, Paris 1988--1989},
   editor       = {Catherine Goldstein},
   publisher    = {Birkh\"auser},
   address      = {Boston},
   series       = {Progress in Mathematics},
   year         = {1990},
   pages        = {27--41}
}

@Article{seysen,
	author = {M. Seysen},
	title = {A probabilistic factorization algorithm with quadratic forms of negative discriminant},
	journal = {Mathematics of computation},
	year = 1987,
	volume = {48},
	pages = {757--780}
}


@inproceedings{LenstraShanks,
 	author = {A.K. Lenstra},
 	title = {On the calculation of regulators and class numbers of quadratic fields},
 	booktitle = {Journ\'{e}es arithm\'{e}tiques},
 	year = {1982},
 	pages = {123--150},
 	publisher = {Cambridge Univ. Press}
 }

@inproceedings{dullmann,
 	author = {J. Buchmann and S. D\"{u}llmann},
 	title = {On the computation of discrete logarithms in class groups},
 	booktitle = {Advances in Cryptology - CRYPTO '90},
	series = {LNCS},
 	year = {1991},
 	pages = {134--139},
 	publisher = {Springer Verlag}
 }

@Article{littlewood,
  	author = {J.E. Littlewood},
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  	year = 1928,
	volume = {27},
  	pages = {358--372}
}

@ARTICLE{lenstra:quad,
  AUTHOR = "H.K. Lenstra",
  TITLE = "On the calculation of regulators and class numbers of quadratic felds",
  JOURNAL = "London Math. Soc. Lecture Note Series",
  VOLUME = "56",
  YEAR = "1982",
  PAGES = "123--150" }

@ARTICLE{buchmann:rep,
  AUTHOR = "J. Buchmann and C. Thiel and H.C. Williams",
  TITLE = "Short representation of quadratic integers",
  JOURNAL = "Computational Algebra and Number Theory, Mathematics and its Applications",
  VOLUME = "325",
  YEAR = "1995",
  PAGES = "159--185" }

@INPROCEEDINGS{BachEulerProd,
  AUTHOR = "E. Bach",
  TITLE = "Improved Approximations for {E}uler Products",
  BOOKTITLE = "Number Theory:  CMS Proc.",
  VOLUME = "15",
  ORGANIZATION = "Amer. Math. Soc., Providence, RI",
  YEAR = "1995",
  PAGES = "13-28"   }

@INPROCEEDINGS{HMiq,
   AUTHOR = "S. Hamdy and B. M{\"o}ller",
   TITLE = "Security of cryptosystems based on class groups of imaginary quadratic orders",
   BOOKTITLE = "Advances in Cryptology - ASIACRYPT 2000",
   SERIES = "Lecture Notes in Computer Science",
   VOLUME = "1976",
   PAGES = "234-247",
   YEAR = "2000" }

@ARTICLE{BWKeyEx,
  AUTHOR = "J. Buchmann and H. C. Williams",
  TITLE = "A key-exchange system based on imaginary quadratic fields",
  JOURNAL = "Journal of Cryptology",
  VOLUME = "1",
  YEAR = "1988",
  PAGES = "107-118" }

@INPROCEEDINGS{BWKeyExReal,
  AUTHOR = "J. Buchmann and H. C. Williams",
  TITLE = "A key-exchange system based on real quadratic fields",
  BOOKTITLE = "CRYPTO '89",
  SERIES = "Lecture Notes in Computer Science",
  YEAR = "1989",
  VOLUME = "435",
  PAGES = "335-343"   }

@INCOLLECTION{CLheur,
  AUTHOR = "H. Cohen and Lenstra, Jr., H. W.",
  TITLE = "Heuristics on class groups of number fields",
  BOOKTITLE = "Number Theory, Lecture notes in Math.",
  PUBLISHER = "Springer-Verlag, New York",
  YEAR = "1983",
  VOLUME = "1068",
  PAGES = "33-62" }

@ARTICLE{Jdl,
  AUTHOR = "Jacobson, Jr., M. J.",
  TITLE = "Computing discrete logarithms in quadratic orders",
  JOURNAL = "Journal of Cryptology",
  YEAR = "2000",
  VOLUME = "13",
  PAGES = "473-492"   }

@ARTICLE{HJWnonint_full,
   AUTHOR = "D. H{\"u}hnlein and Jacobson, Jr., M. J. and D. Weber",
   TITLE = "Towards Practical Non-interactive Public-Key Cryptosystems using
            Non-maximal Imaginary Quadratic Orders",
   JOURNAL = "Designs, Codes and Cryptography",
   YEAR = "2003",
   VOLUME = "30",
   NUMBER = "3",
   PAGES = "281-299"   }

@InProceedings{vollmer,
  author =	  {U. Vollmer},
  title =		  {A note on the {H}ermite Basis Computation of Large
                  Integer Matrices},
  booktitle =	  {International Symposium on Symbolic and Algebraic
                  Computation, {ISSAC} '03},
  year =		  2003,
  editor =	  {J. Rafael Sendra},
  publisher =	  {{ACM} Press},
  pages =		  "255--257"
}

@INPROCEEDINGS{Vdl,
   AUTHOR = "U. Vollmer",
   TITLE = "Asymptotically fast discrete logarithms in quadratic number
            fields",
   BOOKTITLE = "Algorithmic Number Theory --- ANTS-IV",
   SERIES = "Lecture Notes in Computer Science",
   VOLUME = "1838",
   YEAR = "2000",
   PAGES = "581-594" }

@INPROCEEDINGS{Vreg,
   AUTHOR = "U. Vollmer",
   TITLE = "An accelerated {B}uchmann algorithm for regulator computation in real quadratic fields",
   BOOKTITLE = "Algorithmic Number Theory --- ANTS-V",
   SERIES = "Lecture Notes in Computer Science",
   VOLUME = "2369",
   YEAR = "2002",
   PAGES = "148-162" }

@Book{buch_vollmer,
  author = {Johannes Buchmann and Ulrich Vollmer},
  title = {Binary Quadratic Forms: An Algorithmic Approach},
  publisher = {Springer-Verlag},
  year = 2007,
  volume =20,
  series ={Algorithms and Computation in Mathematics}
}

@misc{BJregulator,
	author = {J-F. Biasse and Jacobson, Jr., M. J.},
	title = {Practical improvements to class group and regulator computation of real quadratic fields},
	note = { To appear in ANTS 9 },
	year = { 2010 }
}

@mastersthesis{contini
,title={{Factoring integers with the self-initializing quadratic sieve}}
,booktitle={{Factoring integers with the self-initializing quadratic sieve}}
,author={S. Contini}
,school={University of Georgia}
,year={1997}
}


@article{silverman_MPQS
,note={URL: {\tt http://cr.yp.to/\allowbreak bib/\allowbreak entries.html\#\allowbreak 1987/\allowbreak silverman}}
,author={Robert D. Silverman}
,ISSN={0025--5718}
,journal={Mathematics of Computation}
,MR={88c:11079}
,pages={329--339}
,title={{The multiple polynomial quadratic sieve}}
,volume={48}
,year={1987}
}


@techreport{NIST-keys,
  AUTHOR = "{National Institute of Standards and Technology (NIST)}",
  TITLE = "Recommendation for Key Management - Part 1: General (Revised)",
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  MONTH = "March,",
  YEAR = "2007" }

@ARTICLE{HMSub,
  AUTHOR = "J.L. Hafner and K.S. McCurley",
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  JOURNAL = "J. Amer. Math. Soc.",
  YEAR = 1989,
  VOLUME = 2,
  PAGES = "837-850"
}



@BOOK{LL93,
   AUTHOR = "A.K. Lenstra and Lenstra, Jr., H.W.",
   TITLE = "The Development of the Number Field Sieve",
   PUBLISHER = "Springer-Verlag",
   ADDRESS = "Berlin",
   SERIES = "Lecture Notes in Mathematics",
   YEAR = "1993",
   VOLUME = "1554",   }

@UNPUBLISHED{IJScubing,
   AUTHOR = "L. Imbert and Jacobson, Jr., M. J. and A. Schmidt",
   TITLE = "Fast Ideal Cubing in Imaginary Quadratic Number and Function Fields",
   NOTE = "To appear in to Advances in Mathematics of Communication",
   YEAR = "2010"  }

@ARTICLE{JSWnucomp,
   AUTHOR = "Jacobson, Jr., M.J. and R. Scheidler and H.C. Williams",
   TITLE = "An improved real quadratic field based key exchange procedure",
   JOURNAL = "Journal of Cryptology",
   YEAR = "2006",
   VOLUME = "19",
   PAGES = "211-239"  }

@PHDTHESIS{Hamdy,
  AUTHOR = "S. Hamdy",
  TITLE = "{\"U}ber die {S}icherheit und {E}ffizienz kryptografischer {V}erfahren mit {K}lassengruppen imagin{\"a}r-quadratischer {Z}ahlk{\"o}rper",
  SCHOOL = "Technische Universit{\"a}t Darmstadt",
  YEAR = "2002",
  ADDRESS = "Darmstadt, Germany" }

@INPROCEEDINGS{LVselect,
   AUTHOR = "A.K. Lenstra and E. Verheul",
   TITLE = "Selecting Cryptographic Key Sizes",
   BOOKTITLE = "Proceedings of Public Key Cryptography 2000",
   SERIES = "Lecture Notes in Computer Science",
   VOLUME = "1751",
   PAGES = "446-465",
   YEAR = "2000" }

@BOOK{BVforms,
  AUTHOR = "J. Buchmann and U. Vollmer",
  TITLE = "Binary Quadratic Forms:  An Algorithmic Approach",
  SERIES = "Algorithms and Computation in Mathematics",
  VOLUME = "20",
  PUBLISHER = "Springer-Verlag",
  YEAR = "2007",
  ADDRESS = "Berlin"   }

@article{RSA,
 author = {R. Rivest and A. Shamir and L. Adleman},
 title = {A method for obtaining digital signatures and public-key cryptosystems},
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 issn = {0001-0782},
 pages = {120--126},
 doi = {http://doi.acm.org/10.1145/359340.359342},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@Article{DH,
  author =       {W. Diffie and M. Helman},
  title =        {New Directions in Cryptography},
  journal =      {IEEE Transactions on Information Society},
  year =         1976,
  volume =       22,
  number =       6,
  pages =        {644--654},
  month =        {november}
}

@Article{ECC,
  author =       {N. Koblitz},
  title =        {Elliptic curve cryptosystems},
  journal =      {Mathematics of Computation},
  year =         1987,
  volume =       48,
  pages =        {203--209}
}

@Article{HCC,
  author =       {N. Koblitz},
  title =        {Hyperellitic cryptosystems},
  journal =      {Journal of Cryptology},
  year =         1989,
  volume =       1,
  pages =        {139--150}
}

@inproceedings{Odlyzko,
 author = {A. Odlyzko},
 title = {Discrete logarithms in finite fields and their cryptographic significance},
 booktitle = {Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques},
 year = {1985},
 isbn = {0-387-16076-0},
 pages = {224--314},
 location = {Paris, France},
 publisher = {Springer-Verlag New York, Inc.},
 address = {New York, NY, USA},
 }

@INPROCEEDINGS {thome,
	AUTHOR="E. Thom\'e",
	TITLE="Computation of Discrete Logarithms in {GF}(2\^{}607)",
	BOOKTITLE={Advances in Cryptology, Asiacrypt'2001},
        PUBLISHER={Springer-Verlag},
        SERIES={Lecture Notes in Computer Science},
        NUMBER={2369},
	PAGES={107--124},
        YEAR = {2001}
}

@inproceedings{claus,
  author    = {C. Fieker and
               D. Stehl{\'e}},
  title     = {Short Bases of Lattices over Number Fields},
  booktitle = {Algorithmic Number Theory, 9th International Symposium, ANTS-IX, Nancy, France, July 19-23, 2010. Proceedings},
  year      = {2010},
  pages     = {157-173},
 publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {6197},
  year      = {2010}
}


@incollection {lattice_sieve,
   author = {J. Pollard},
   title = {The lattice sieve},
   booktitle = {The development of the number field sieve},
   series = {Lecture Notes in Mathematics},
   editor = {A. Lenstra and H. K. Lenstra},
   publisher = {Springer Berlin / Heidelberg},
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   year = {1993}
}

@inproceedings{NF_sieve,
 author = {Lenstra, A. K. and Lenstra,Jr., H. W. and Manasse, M. S. and Pollard, J. M.},
 title = {The number field sieve},
 booktitle = {STOC '90: Proceedings of the twenty-second annual ACM symposium on Theory of computing},
 year = {1990},
 isbn = {0-89791-361-2},
 pages = {564--572},
 location = {Baltimore, Maryland, United States},
 doi = {http://doi.acm.org/10.1145/100216.100295},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@Book{enge_phd,
   author       = {A. Enge},
   title        = {Hyperelliptic cryptosystems: efficiency and
                   subexponential attacks},
   publisher    = {Books on Demand},
   year         = 2000
}

@Article{Enge02,
  author =       {A. Enge},
  title =        {Computing Discrete Logarithms in High-Genus Hyperelliptic
                  {J}acobians in Provably Subexponential Time},
  journal =      {Mathematics of Computation},
  year =         {2002},
  volume =       {71},
  pages =        {729--742}
}


@inproceedings {gaudry,
   author       = {Pierrick Gaudry},
   title        = {An Algorithm for Solving the Discrete Log Problem on
                   Hyperelliptic Curves},
   booktitle    = {Advances in Cryptology --- EUROCRYPT 2000},
   editor       = {Bart Preneel},
   publisher    = {Springer-Verlag},
   address      = {Berlin},
   series       = {Lecture Notes in Computer Science},
   volume       = {1807},
   isbn         = {3-540-67517-5},
   year         = {2000},
   pages        = {19--34}
}

@inproceedings {AdDeHu94,
   author       = {L. M. Adleman and J. DeMarrais and M.-D. Huang},
   title        = {A Subexponential Algorithm for Discrete Logarithms over the
                  Rational Subgroup of the {J}acobians of Large Genus
                  Hyperelliptic Curves over Finite Fields},
   booktitle    = {Algorithmic Number Theory},
   editor       = {Leonard M. Adleman and Ming-Deh Huang},
   publisher    = {Springer-Verlag},
   address      = {Berlin},
   series       = {Lecture Notes in Computer Science},
   volume       = {877},
   year         = {1994},
   pages        = {28--40}
}



@INPROCEEDINGS{nonMaxOrder_1,
    author = {D, Huhnlein and M. Jacobson and S. Paulus and T. Takagi},
    title = {A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption},
    booktitle = {Advances in Cryptology - EUROCRYPT '98},
    year = {1998},
    pages = {294--307},
    publisher = {Springer}
}

@article{nonMaxOrder_2,
  author    = {S. Paulus and
               T. Takagi},
  title     = {A New Public-Key Cryptosystem over a Quadratic Order with
               Quadratic Decryption Time},
  journal   = {J. Cryptology},
  volume    = {13},
  number    = {2},
  year      = {2000},
  pages     = {263--272}
}

@inproceedings{nonMaxOrder_3,
 author = {J. Buchmann and K. Sakurai and T. Takagi},
 title = {An I{N}{D}-{C}{C}{A}2 Public-Key Cryptosystem with Fast Decryption},
 booktitle = {ICISC '01: Proceedings of the 4th International Conference Seoul on Information Security and Cryptology},
 year = {2002},
 isbn = {3-540-43319-8},
 pages = {51--71},
 publisher = {Springer-Verlag},
 address = {London, UK},
 }

@inproceedings{nonMaxOrder_4,
  author    = {M. Jacobson and
               R. Scheidler and
               D. Weimer},
  title     = {An Adaptation of the {N}{I}{C}{E} Cryptosystem to Real Quadratic
               Orders},
   booktitle    = {Progress in Cryptology - AFRICACRYPT 2008, First International
               Conference on Cryptology in Africa, Casablanca, Morocco,
               June 11-14, 2008. Proceedings},
 editor    = {Serge Vaudenay},
  year      = {2008},
  pages     = {191--208},
  series    = {Lecture Notes in Computer Science},
  volume    = {5023}
}

@inproceedings{arb_dim_2,
 author = {J. Buchmann and S. Paulus},
 title = {A One Way Function Based on Ideal Arithmetic in Number Fields},
 booktitle = {CRYPTO '97: Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology},
 year = {1997},
 isbn = {3-540-63384-7},
 pages = {385--394},
 publisher = {Springer-Verlag},
 address = {London, UK},
 }

@inproceedings{arb_dim_3,
 author = {A. Meyer and S. Neis and T. Pfahler},
 title = {First Implementation of Cryptographic Protocols Based on Algebraic Number Fields},
 booktitle = {ACISP '01: Proceedings of the 6th Australasian Conference on Information Security and Privacy},
 year = {2001},
 isbn = {3-540-42300-1},
 pages = {84--103},
 publisher = {Springer-Verlag},
 address = {London, UK},
 }

@article{arb_dim_1,
 author = {I. Biehl and J. Buchmann and S. Hamdy and A. Meyer},
 title = {A Signature Scheme Based on the Intractability of Computing Roots},
 journal = {Des. Codes Cryptography},
 volume = {25},
 number = {3},
 year = {2002},
 issn = {0925-1022},
 pages = {223--236},
 doi = {http://dx.doi.org/10.1023/A:1014927327846},
 publisher = {Kluwer Academic Publishers},
 address = {Norwell, MA, USA},
 }


@inproceedings{DHIES,
 author = {M. Bellare and P. Rogaway},
 title = {Minimizing the use of random oracles in authenticated encryption schemes},
 booktitle = {ICICS '97: Proceedings of the First International Conference on Information and Communication Security},
 year = {1997},
 isbn = {3-540-63696-X},
 pages = {1--16},
 publisher = {Springer-Verlag},
 address = {London, UK},
 }

@inproceedings{ElGamal,
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 title = {A public key cryptosystem and a signature scheme based on discrete logarithms},
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 year = {1985},
 isbn = {0-387-15658-5},
 pages = {10--18},
 location = {Santa Barbara, California, United States},
 publisher = {Springer-Verlag New York, Inc.},
 address = {New York, NY, USA},
 }

@inproceedings{FiatShamir,
  author    = {A. Fiat and
               A. Shamir},
  title     = {How to Prove Yourself: Practical Solutions to Identification
               and Signature Problems},
 editor    = {A. Odlyzko},
booktitle     = {Advances in Cryptology - CRYPTO '86, Santa Barbara, California,
               USA, 1986, Proceedings},
series    = {Lecture Notes in Computer Science},
  volume    = {263},
 publisher = {Springer},
  year      = {1986},
  pages     = {186-194}
}


@article{fiat_real,
  author    = {J. Buchmann and M. Maurer and B. M\"{o}ller},
  title     = {Cryptography
based on number fields with large regulator},
  journal   = {Journal de Th\'{e}orie des Nombres de Bordeaux},
  volume    = {12},
  year      = {2000},
  pages     = {293--307}
}

@proceedings{thomeDLP,
  editor    = {M. G. Parker},
  booktitle = {Cryptography and Coding, 12th IMA International Conference,
               Cryptography and Coding 2009, Cirencester, UK, December
               15-17, 2009. Proceedings},
author      = {A. Joux and
               R. Lercier and
               D. Naccache and
               E. Thom{\'e}},
  title     = {Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete
               Logarithms},
  publisher = {Springer},
  series    = {Lecture Notes in Computer Science},
  volume    = {5921},
  year      = {2009},
  isbn      = {978-3-642-10867-9},
  ee        = {http://dx.doi.org/10.1007/978-3-642-10868-6},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


@Book{Cox89,
  author =       {D. A. Cox},
  title =        {Primes of the form $x^2+n y^2$},
  publisher =    {John Wiley \& Sons},
  year =         1989
}


@article{bilu_hanrot,
title = "Solving Thue Equations of High Degree",
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}


@manual{pari,
      organization = "{The PARI~Group}",
      title        = "{PARI/GP, version {\tt 2.5.0}}",
      year         = 2011,
      address      = "Bordeaux",
      note         = "http://pari.math.u-bordeaux.fr/"
    }

@inproceedings{fincke_pohst,
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} 

@article{poza,
  author={M. Pohst and H. Zassenhaus},
  title={{\"U}ber die {B}erechnung
    von {K}lassenzahlen und {K}lassengruppen algebraischer {Z}ahlk{\"o}rper},
  journal={J. Reine Angew. Math.},
  volume={361},
  year={1985},
  pages={50--72}
}

@article{min-rep,
  author={C. Fieker},
  title={Minimizing representations over number fields II: 
      Computations in the {B}rauer group},
  journal={J. Algebra},
  volume={322},
  number={3},
  pages={752--765},
  year={2009}
}
@PHDTHESIS{hess,
  AUTHOR = "F. Hess",
  TITLE = "Zur Divisorklassengruppenberechnung in globalen Funktionenk{\"o}rpern",
  SCHOOL = "Technische Universit{\"a}t Berlin", 
  YEAR = "1999",
  ADDRESS = "Berlin, Germany" }

@article{tscheb,
  author={N. Cebotarev},
  title={Die {B}estimmung der {D}ichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen {S}ubstitutionsklasse geh{\"o}ren},
  journal={Math. Ann.},
  volume={95},
  pages={191--228},
  year={1926}
}


